Hydrostatic Pressure and its Measurement

Hydrostatic refers to any fluid that is at rest. While pressure refers to the concentration of force in a given area. Hydrostatic Pressure together refers to the presence of pressure in fluids at rest. Fluids apply pressure on every side. The objective is to understand the correlation of a fluid with its depth and body at rest. 

The word ‘hydrostatic’ is derived from the Greek word “hydro,” meaning water, and “statikós,” meaning to make a stand. Hydrostatic pressure applies to all fluids, liquid or gas. 

Hydrostatic Pressure and its Measurements

Hydrostatic pressure refers to the fluid pressure at rest, and it is caused due to gravity. Hydrostatic pressure and its measurements are complicated as hydrostatic pressure is easily affected by gravity, open-lid tanks, atmospheric pressure, etc.

Hydrostatic pressure can be measured in Pascal (Pa). The Pascal SI unit is named after Blaise Pascal. Pascal equals 1 N per square metre or 1 KG per metre per second squared.  

Applications of Hydrostatic Pressure

• Uses of hydrostatic formulas tend to be helpful in hydraulics. 

• Hydrostatic pressure is used practically to determine the fluid pressure in vessels such as cylinders, boilers, tube pipes, etc. 

• Hydrostatic formulas can assist you in calculating the predetermined pressure. 

• Predetermined pressure can further help you to conclude the strength of a vessel. 

• Another application of Hydrostatic Pressure is that it helps make the fluid vessels leak free for smooth functioning. 

• Hydrostatic pressure is also used in fields such as transportation and storage. 

Hydrostatic Pressure Formula

The hydrostatic pressure formula is as follows:

                         P = pgh 

where, 

P = Hydrostatic Pressure (Kg per metre/s^2) or 1 Newton or Pascal. 

p = density (M/D^3) or (lbs/ft^3) or (Kg/m^3). 

g = gravity (D/T^2) or (ft/s^2) or (m/s^2). 

h = height (D) or (ft) or (m). 

Hydrostatic Pressure Example

The hydrostatic pressure example is as follows:

Example: Calculate the depth of a vessel if the pressure at the bottom is 1,20,000 Pa. 

Answer: Given, 

Hydrostatic pressure = 1,20,000 Pa

Gravity = 9.81 m/s^2

Water density = 1000 kg/m^2

Putting the values in P = pgh

We get,

              1,20,000 = (1,000) (9.81) (h)

              1,20,000 = 9,810 (h)

              1,20,000/9810 = h

So,         h =  12.2324159 metres. 

The difference in Hydrostatic Pressure Formula

The difference in the Hydrostatic pressure formula is as follows:

              Change in pressure = p.g.change in height 

where, 

Change in pressure = Pressure at a top differential to at the bottom. If the tank/container is open, the pressure would equal that of the atmospheric pressure at the tank opening. 

Change height = It is simply the depth. 

Example: Calculate the water pressure in the house tap if the open tank is placed 45 metres above the house and is 5 metres deep. Atmospheric pressure is 101,325 Pa. 

Answer: Given,

Gravity = 9.81 m/s^2

Water density = 1000 kg/m^2

Total height = 45+5 = 50 metres. 

Assuming the pressure at the top  Patm and pressure at the house tap as Phouse. 

Putting the values in Change in pressure = p.g.change in height 

We get,    

             Phouse – Patm = (1,000) (9.81) (50)

             Phouse – 101,325 = (9,810) (50)

             Phouse – 101,325 = 4,90,500

             Phouse = 4,90,500 + 101,325

So,        Phouse = 5,91,825 Pa. 

Note: Density x Gravity x Difference between two points is a formula to find pressure difference however, without adding the value Patm, the formula becomes an equation to measure the gauge pressure.

Conclusion

Hydrostatic pressure is used in our day to day lives, and its applications are almost everywhere. Why bubbles float, why you drown, why titanic sank etc., questions can be understood through a great understanding of hydrostatic pressure. Hydrostatic pressure also has some relative phenomena, such as Pascal’s principle and Archimedes’s principle. 

Hydrostatic pressure has impressive applications in mechanics, geophysics, meteorology, medicines, submarines, underwater and space expeditions, etc. The unit to measure Hydrostatic pressure is named after Blaise Pascal, A french mathematician. Blaise also is the prodigy behind Pascal’s law or Pascal’s principle.